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Simplifying 9x(4x + -1) = 11 Reorder the terms: 9x(-1 + 4x) = 11 (-1 * 9x + 4x * 9x) = 11 (-9x + 36x2) = 11 Solving -9x + 36x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -9x + 36x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -9x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3055555556 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.3055555556' to each side of the equation. -0.3055555556 + -0.25x + 0.3055555556 + x2 = 0 + 0.3055555556 Reorder the terms: -0.3055555556 + 0.3055555556 + -0.25x + x2 = 0 + 0.3055555556 Combine like terms: -0.3055555556 + 0.3055555556 = 0.0000000000 0.0000000000 + -0.25x + x2 = 0 + 0.3055555556 -0.25x + x2 = 0 + 0.3055555556 Combine like terms: 0 + 0.3055555556 = 0.3055555556 -0.25x + x2 = 0.3055555556 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.3055555556 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.3055555556 + 0.015625 Combine like terms: 0.3055555556 + 0.015625 = 0.3211805556 0.015625 + -0.25x + x2 = 0.3211805556 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.3211805556 Calculate the square root of the right side: 0.566727938 Break this problem into two subproblems by setting (x + -0.125) equal to 0.566727938 and -0.566727938.Subproblem 1
x + -0.125 = 0.566727938 Simplifying x + -0.125 = 0.566727938 Reorder the terms: -0.125 + x = 0.566727938 Solving -0.125 + x = 0.566727938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.566727938 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.566727938 + 0.125 x = 0.566727938 + 0.125 Combine like terms: 0.566727938 + 0.125 = 0.691727938 x = 0.691727938 Simplifying x = 0.691727938Subproblem 2
x + -0.125 = -0.566727938 Simplifying x + -0.125 = -0.566727938 Reorder the terms: -0.125 + x = -0.566727938 Solving -0.125 + x = -0.566727938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.566727938 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.566727938 + 0.125 x = -0.566727938 + 0.125 Combine like terms: -0.566727938 + 0.125 = -0.441727938 x = -0.441727938 Simplifying x = -0.441727938Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.691727938, -0.441727938}
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